



Hi Ken,
I have two thoughts; others should please correct me if I am wrong about either of these.
1.) The random effects are the condition modes (not means) in linear mixed models as well,
2.) The variance estimate from the model output can be interpreted as the estimated variance in the population from which the random effects in your sample are assumed to be draws -- NOT the variance of the random effects ("BLUPs") in your sample themselves. The simple variance of the BLUPs will in general be lower than the variance estimate stated in the model output due to shrinkage of the BLUPs toward the estimated population mean. 
Jake

> From: kkelley@nd.edu
> To: Thierry.ONKELINX@inbo.be
> Date: Tue, 24 Jul 2012 14:38:20 -0400
> CC: r-sig-mixed-models@r-project.org
> Subject: Re: [R-sig-ME] mean and variance of random effects in glmer
> 
> Hi Thierry,
> 
> Thanks for your thoughts on this. I hadn't considered quasi-separation, but I don't think that is it. Actually, the issue is that I slipped into thinking that the random effects were the conditional means (like in a linear mixed effects model). Rather, they are the conditional modes. Thus, the mean of the random effects need not be zero as I initially expected (and as would be the case in a linear mixed effects model). 
> 
> But, I still expected the variance of the random effects to match the output (it is 18.9 in the output yet 7.8 when I calculate it on the random effects directly). 
> 
> Best wishes,
> Ken
> 
> 
> 
> 
> 
> On Jul 24, 2012, at 5:23 AM, "ONKELINX, Thierry" <Thierry.ONKELINX@inbo.be> wrote:
> 
> > Dear Ken,
> > 
> > Very large variance for the random effect in a binomial glmer is an indication for (quasi-)complete separation. Here is some info on that issue: http://www.ats.ucla.edu/stat/mult_pkg/faq/general/complete_separation_logit_models.htm
> > 
> > If the values of Problem and Across are constant within each level of PID, I would aggregate the data (sum per PID) and then use a simple glm()
> > 
> > Best regards,
> > 
> > Thierry
> > 
> > ir. Thierry Onkelinx
> > Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest, 
> > team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
> > Kliniekstraat 25
> > 1070 Anderlecht
> > Belgium
> > + 32 2 525 02 51
> > + 32 54 43 61 85
> > Thierry.Onkelinx@inbo.be
> > www.inbo.be
> > 
> > To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of.
> > ~ Sir Ronald Aylmer Fisher
> > 
> > The plural of anecdote is not data.
> > ~ Roger Brinner
> > 
> > The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data.
> > ~ John Tukey
> > 
> > -----Oorspronkelijk bericht-----
> > Van: r-sig-mixed-models-bounces@r-project.org [mailto:r-sig-mixed-models-bounces@r-project.org] Namens Ken Kelley
> > Verzonden: dinsdag 24 juli 2012 8:29
> > Aan: r-sig-mixed-models@r-project.org
> > Onderwerp: [R-sig-ME] mean and variance of random effects in glmer
> > 
> > Hi everyone,
> > 
> > I'm fitting a straightforward glmer model with the family=binomial. I expected the mean of the random effect for the intercept to be near zero, but that isn't the case, as the mean is .91:
> > 
> >> (model.3 <- glmer(TA ~ 1 + Problem + Across + (1|PID), data=Data.Timed, family = binomial, nAGQ=100))
> > Generalized linear mixed model fit by the adaptive Gaussian Hermite approximation
> > Formula: TA ~ 1 + Problem + Across + (1 | PID)
> >   Data: Data.Timed
> >   AIC   BIC logLik deviance
> > 158.8 172.9 -75.38    150.8
> > Random effects:
> > Groups Name        Variance Std.Dev.
> > PID    (Intercept) 18.869   4.3439
> > Number of obs: 256, groups: PID, 64
> > 
> > Fixed effects:
> >            Estimate Std. Error z value Pr(>|z|)
> > (Intercept)  -1.1328     0.7304  -1.551   0.1209
> > Problem      -0.5864     0.2449  -2.394   0.0167 *
> > Across       -1.3768     0.4280  -3.217   0.0013 **
> > ---
> > Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> > 
> > Correlation of Fixed Effects:
> >        (Intr) Problm
> > Problem -0.390
> > Across  -0.208 -0.150
> > 
> > That is, I'm doing a mixed effects logistic regression. The PID is the participant ID; there are 4 Problems (essentially timepoints: 0, 1, 2, 3) and Across is a time-varying covariate (0, 1, 2, or 3).
> > 
> > The mean of the random effects is:
> >> colMeans(ranef(model.3)$PID[])
> > (Intercept)
> >  0.9137307
> > 
> > Additionally, the variance of the random effect is in the model output as 18.869, yet when I calculate the variance of the random effects directly, I get a much smaller value:
> >> var(ranef(model.3)$PID[])
> >            (Intercept)
> > (Intercept)    7.806402
> > 
> > Should I be surprised by either of the issues I note above? My concern is that I was planning on plotting the model implied curves using the fixed effects (so that the curves would represent an individual specific trajectory for a participant with a random effect of 0). Yet, there are no individuals with a random effect of zero and the mean is not zero. Thus, such a plot doesn't seem as useful as I initially thought it would.
> > 
> > Thanks for any thoughts on this,
> > Ken
> > 
> > 
> > 
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